This is a short overview on gentzenization of some distributive contraction-less relevant logics.... more This is a short overview on gentzenization of some distributive contraction-less relevant logics. We analyze problems which may occur in formulating sequent calculi for the logics RW + and RW and we give their solutions, the well-known as well as some recent ones.
A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The ... more A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The operational rules of NI are obtained by the translation from Gentzen’s calculus LJ and the normalization is proved, via translations from sequent calculus derivations to natural deduction derivations and back.
This paper presents a sequent calculus for the positive relevant logic with necessity and a proof... more This paper presents a sequent calculus for the positive relevant logic with necessity and a proof that it admits the elimination of cut.
A normalizable natural deduction formulation, with subformula property, of the implicative fragme... more A normalizable natural deduction formulation, with subformula property, of the implicative fragment of classical logic is presented. A traditional notion of normal deduction is adapted and the corresponding weak normalization theorem is proved. An embedding of the classical logic into the intuitionistic logic, restricted on propositional implicational language, is described as well. We believe that this multiple-conclusion approach places the classical logic in the same plane with the intuitionistic logic, from the proof-theoretical viewpoint.
This is a short overview on gentzenization of some distributive contraction-less relevant logics.... more This is a short overview on gentzenization of some distributive contraction-less relevant logics. We analyze problems which may occur in formulating sequent calculi for the logics RW + and RW and we give their solutions, the well-known as well as some recent ones.
A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The ... more A natural deduction system NI, for the full propositional intuitionistic logic, is proposed. The operational rules of NI are obtained by the translation from Gentzen’s calculus LJ and the normalization is proved, via translations from sequent calculus derivations to natural deduction derivations and back.
This paper presents a sequent calculus for the positive relevant logic with necessity and a proof... more This paper presents a sequent calculus for the positive relevant logic with necessity and a proof that it admits the elimination of cut.
A normalizable natural deduction formulation, with subformula property, of the implicative fragme... more A normalizable natural deduction formulation, with subformula property, of the implicative fragment of classical logic is presented. A traditional notion of normal deduction is adapted and the corresponding weak normalization theorem is proved. An embedding of the classical logic into the intuitionistic logic, restricted on propositional implicational language, is described as well. We believe that this multiple-conclusion approach places the classical logic in the same plane with the intuitionistic logic, from the proof-theoretical viewpoint.
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Papers by Mirjana Ilic